RU2713720C1 - Method for checking the probability of reliable measurements - Google Patents

Abstract

FIELD: measuring equipment.

SUBSTANCE: invention relates to measurement techniques when exposed to interference, for example, in laser range-finding equipment or in burglar alarm systems. Method for verifying probability p of reliable measurements of device, consisting in n-multiple repetition of measurements, determining the number of m unreliable measurements and comparing m with the maximum permissible value of the number of unreliable measurements m_mp(n), checking is carried out in stages, namely, at the first stage, performing series n₁=(1+t)p measurements, where t is the confidence coefficient, and if number of unreliable measurements does not exceed m₁=0, then device is considered serviceable and check is stopped, if m₁=1, the measurement series is continued to number n₂=(2+t√2)p, and if the number of unreliable measurements does not exceed m₂=1, then the device is considered to be serviceable and the check is terminated, if m₂=2, the measurement series is continued to number n₃=(3+t√3)p, and if the number of unreliable measurements does not exceed m₃=2, then the device is considered to be serviceable and the check is terminated, similarly, the series of measurements is continued to n_k=(k+t√k)p and the device is considered to be serviceable if the number of unreliable measurements in the series m_k≤(k-1), otherwise the device is considered not to have passed the test.

EFFECT: technical result consists in ensuring maximum reliability of inspection with minimum volume of tests.

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Description

The present invention relates to a measurement technique when exposed to interference, for example, in laser ranging, in alarm systems and other areas with increased requirements for the reliability of measurements.

Known methods for remote measurements associated with the selection of weak signals [1], which include sensing a remote object with laser pulses, receiving the signals reflected by the object and determining the parameters of the reflected signal, which are used to judge the characteristics of the remote object, for example, the distance to it. The results of such procedures should satisfy the given probability of a reliable measurement.

Known video analysis tools in CCTV systems [2], which detect signals from remote sensors. In this case, it is also required to provide a given probability of correct identification of the signal.

Methods are also known for stabilizing the frequency of false positives at an acceptable level during the measurement process [3].

A feature of these methods are conflicting requirements for the detection threshold of received signals. On the one hand, this threshold should be as low as possible to ensure maximum sensor sensitivity. On the other hand, the response threshold should be high enough to minimize the likelihood of a false alarm from internal sensor noise and other interference. Thus, the probability of a reliable measurement should be as close as possible to the allowable limit, which imposes strict requirements on the accuracy of control methods proportional to the volume of tests.

Closest to the technical nature of the proposed method is a method of checking the probability of a reliable measurement, implemented in the laser range finder LPR-1 [4]. This device is checked for compliance with the requirements for the probability of a reliable measurement by 10 measurements, of which at least 9 must be reliable.

With higher requirements for the likelihood of reliable measurement, the required test volume increases significantly, which leads to an increase in the test duration and a reduction in the resource of the tested product.

The objective of the invention is to ensure maximum reliability of the test with a minimum amount of testing.

измерений, где t - доверительный коэффициент, и если количество недостоверных измерений не превышает m₁=0, то прибор считают исправным и проверку прекращают, если m₁=1, то серию измерений продолжают до количества

и если количество недостоверных измерений не превышает m₂=1, то прибор считают исправным и проверку прекращают, если m₂=2, то серию измерений продолжают до количества

и если количество недостоверных измерений не превышает m₃=2, то прибор считают исправным и проверку прекращают, аналогичным образом серию измерений продолжают до

и считают прибор исправным, если количество недостоверных измерений в серии m_k≤(k-1), в противном случае прибор считают не выдержавшим проверку.This problem is solved due to the fact that in the known method of checking the probability p of reliable measurements of the device, which consists in n-fold repetition of measurements, determining the number m of false measurements and comparing m with the maximum permissible value of the number of false measurements m _pd (n), the verification is carried out in stages namely, at the first stage a series is produced

measurements, where t is the confidence coefficient, and if the number of false measurements does not exceed m ₁ = 0, then the device is considered serviceable and the test is stopped, if m ₁ = 1, then the series of measurements is continued to the number

and if the number of false measurements does not exceed m ₂ = 1, then the device is considered serviceable and the test is stopped, if m ₂ = 2, then the series of measurements is continued to the number

and if the number of false measurements does not exceed m ₃ = 2, then the device is considered serviceable and the test is stopped, in a similar way the series of measurements is continued until

and they consider the device serviceable if the number of inaccurate measurements in the series is m _k ≤ (k-1), otherwise the device is considered to have failed the test.

The technical result of the invention is to ensure high reliability of the measuring instrument with a guaranteed minimum probability of an unreliable measurement and with a minimum number of measurements during the test.

In FIG. 1 shows a diagram of a device that implements the method. In FIG. 2 is a diagram of a statistical spread of test results.

According to FIG. 1, the device contains a receiver 1, the input of which is a mixture of a signal with noise, and the counter m of false measurements 2 and a resolver 3 are connected in series. The counter n of the operating time 4 is connected to the other input of the resolver 4. The outputs of program unit 5 are connected to the receiver, the counter n and counter m. the output of the resolver 3 is connected to the program unit 5. Another output of the solver is the output of the system.

The method is as follows.

Запускают контрольную серию измерений и производят подсчет недостоверных измерений m путем их регистрации в счетчике 2. При достижении наработки n=n₁ с помощью решающего устройства 3 проверяют условие m=0 и если это условие выполняется, то считают вероятность недостоверных измерений в норме и заканчивают проверку. Если m>0, то это значение регистрируют в решающем устройстве и продолжают испытания до наработки

Если при этом m=k-1, то считают вероятность недостоверных измерений в норме и заканчивают проверку. В противном случае считают, что прибор не выдержал испытаний. Предельное количество k измерений, необходимое для гарантированного подтверждения результата, устанавливают исходя из принятых доверительных условий.Before starting the control series of measurements, using the program unit 5, the counter m of unreliable measurements 2 and the counter n of operating time 4 are reset to zero. At the same time, the initial state is set in the solving device 3

The control series of measurements is started and the false measurements m are calculated by registering them in the counter 2. When the operating time n = n _{1 is} reached, the condition m = 0 is checked using the resolver 3 and if this condition is met, then the probability of the false measurements is normal and the check is completed . If m> 0, then this value is recorded in the solver and the tests are continued until operating hours

If in this case m = k-1, then the probability of false measurements is considered normal and the test is completed. Otherwise, it is believed that the device did not pass the tests. The limit number k of measurements necessary for guaranteed confirmation of the result is established on the basis of the accepted confidence conditions.

The relative frequency of inaccurate measurements corresponds to the Bernoulli scheme for random alternative events and obeys the binomial distribution [5].

Moreover, the mathematical expectation of the estimate W of the frequency of false measurements m / n in a series of n tests

The variance of the estimate of the frequency of false measurements

where p is the expected probability of the event.

Standard deviation of the estimate

Figure 2 shows the position of the estimate W relative to the true value of the probability p, as well as the density distribution diagram of the estimates with standard deviation σ and confidence limits ± tσ.

When assessing W the probability of an invalid measurement by calculating the relative frequency of invalid measurements [5] as the ratio of the number m * of invalid measurements and the total volume of the series n, the acceptance quantity m * = m * _pr is determined by the expression

Where

p is the given probability of an unreliable measurement

- доверительный коэффициент.

- confidence coefficient.

For the minimum significant value m * _np = 1, the minimum volume of the series follows from (4)

Where

Example 1

p = 0.01;

According to (5), n _min = 1091.

According to the method of interval estimates [5], the upper boundary of the confidence probability for n >> 1 is described by the formula

where W = m / n;

t is a confidence coefficient determined from the expression

Ф (t) = γ / 2:

γ is the confidence probability;

Φ (t) is the Laplace function.

For W << 1, expression (6) is simplified

where from

The proposed technical solution consists in the phased application of criterion (8) in the process of checking the probability of a reliable measurement for each of the unreliable results.

At the first stage, measurements are carried out in an amount sufficient to obtain, with a given confidence probability, one unreliable result.

Example 2

m is 1; p = 0.01; t = 2 (corresponds to the probability γ = 0.95).

In accordance with the formula (8)

Similarly for m = 2

This means that if there is one unreliable measurement in the first series, an additional n ₂ * = n ₂ -n ₁ = 483-300 = 183 measurements are carried out.

In this case, the average number of measurements when testing serial production according to the results of a two-stage verification

Example 3

In the conditions of example 2 n _cf = 300 + 0.05-183 = 309.

The influence of the third and subsequent stages of the test on n _cf. on the average number of measurements can be neglected, since the decreasing factor (1-γ) is included in the expression to the power of 2, etc.

From the obtained results it can be seen that the proposed technical solution, in comparison with the known ones, allows to reduce the average operating time n _sr during the tests from 1091 (example 1) to 309 (example 3), that is, more than three times.

Thus, the proposed method is a solution to the problem and provides maximum reliability checks with a minimum amount of testing.

Sources of information

1. The striker. Using lasers to measure distances. "Foreign Radio Electronics", 1964, No. 3.

2. Guidelines R 78.36.030-2013. Application of video analysis software in CCTV systems.

3. Vilner V.G. Design threshold devices with noise stabilization threshold. // Optical-mechanical industry. - 1984 - No. 5, - S. 39-41.

4. Laser reconnaissance device LPR-1. Technical description and instruction manual. - prototype.

5. Gmurman V.E. Theory of Probability and Mathematical Statistics. M. "Higher School", 1977 - S. 66.

Claims (1)

A method of checking the probability p of reliable measurements of the device, which consists in n-fold repeating measurements, determining the number m of invalid measurements and comparing m with the maximum permissible value of the number of false measurements m _pd (n), characterized in that the verification is carried out in stages, namely, on the first stage produce a series

measurements, where t is the confidence coefficient, and if the number of false measurements does not exceed m ₁ = 0, then the device is considered serviceable and the test is stopped, if m ₁ = 1, then the series of measurements is continued to the number

, and if the number of false measurements does not exceed m ₂ = 1, then the device is considered serviceable and the test is stopped, if m ₂ = 2, then the series of measurements is continued to the number

, and if the number of false measurements does not exceed m ₃ = 2, then the device is considered serviceable and the test is stopped, in a similar way, the series of measurements is continued until

and they consider the device serviceable if the number of inaccurate measurements in the series is m _k ≤ (k-1), otherwise the device is considered to have failed the test.

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